$\bar{\psi} \psi$-condensate in constant magnetic fields

TL;DR

This paper solves the Dirac equation in constant magnetic fields across different dimensions, calculates the fermion condensate from first principles, and compares results with existing literature to highlight potential physical applications.

Contribution

It provides a first-principles calculation of the $ar{ ext{ extpsi}} ext{ extpsi}$-condensate in magnetic fields for both parity conserving and violating theories in various dimensions.

Findings

Calculated condensate for arbitrary magnetic field strength.

Compared results with existing literature for specific cases.

Discussed relevance to physical applications.

Abstract

We solve Dirac equation in the presence of a constant magnetic field in (3+1)- and (2+1)-dimensions. Quantizing the fermion field, we calculate $\bar{\psi} \psi$-condensate from first principles for parity conserving and violating Lagrangians for arbitrary field strength. We make comparison with the results already known in the literature for some particular cases and point out the relevance of our work for possible physical applications.